Performance limitations of discrete-time systems in tracking sinusoidal signals

This paper studies the performance limitation of an LTI multivariable discrete-time system in tracking a reference signal which is a linear combination of a step signal and several sinusoids with different frequencies. It attempts to extend some recent results for continuous-time systems on the same issue. The tracking performance is measured by the energy of the error between the output of the plant and the reference signal. Our purpose is to find the fundamental limitation for the attainable tracking performance, under any control structure and parameters, in terms of the characteristics and structural parameters of the given plant as well as the reference signal under consideration. It is shown that this fundamental limitation depends on the interaction between the reference signal and the non-minimum phase zeros of the plant and their frequency dependent directional information.